preparation

Make cookies:

Preheat oven to 325°F with rack in middle. Butter a large baking sheet.

Pulse hazelnuts, sugar, flour, cocoa powder, baking soda, salt, cinnamon, and cloves in a food processor until nuts are finely chopped, then add butter and zest and pulse until mixture resembles coarse meal with some small (roughly pea-size) butter lumps. Add juice and liqueur and pulse until dough comes together into a ball but is still crumbly. Form level tablespoons of dough into balls and flatten to about 1 1/2 inches in diameter, arranging 1 inch apart on baking sheet.

Bake cookies until puffed and slightly cracked, about 15 minutes. Transfer to a rack to cool completely.

Make icing while cookies cool:

Whisk together all icing ingredients until smooth.

Dip tops of cooled cookies into icing and transfer to a wax-paper-lined baking sheet. Let stand until icing is set, about 1 hour.